To determine which of the given points is on the graph of the function \( y = (2z + 1) - 4 \), we first need to simplify the function. The ' indicates differentiation, and it's a little unclear in this context, so let’s treat it simply as the expression given rather than perform differentiation.
Thus, the function can be rewritten as:
\[ y = 2z + 1 - 4 \]
Simplifying this gives:
\[ y = 2z - 3 \]
Next, we can check each point to see if it satisfies this equation.
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For the point \((-1, -5)\): \[ y = 2(-1) - 3 = -2 - 3 = -5 \quad \text{(this point lies on the graph)} \]
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For the point \((1, 2)\): \[ y = 2(1) - 3 = 2 - 3 = -1 \quad \text{(this point does NOT lie on the graph)} \]
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For the point \((0, -2)\): \[ y = 2(0) - 3 = 0 - 3 = -3 \quad \text{(this point does NOT lie on the graph)} \]
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For the point \((-1, -3)\): \[ y = 2(-1) - 3 = -2 - 3 = -5 \quad \text{(this point does NOT lie on the graph)} \]
From this analysis, only the point \((-1, -5)\) satisfies the equation \( y = 2z - 3 \).
The correct answer is:
O (-1,-5)